CUMULATIVITY AND RATIONALITY IN SEMANTICS OF NORMAL LOGIC PROGRAMS

Our aim in this paper is to classify and review the different semantics for logic programs with negation that have been considered in the last years. We look from a more structural point of view at these semantics. As they induce nonmonotonic entailment relations ''squiggley horizontal right perpendicular'', we ask for the properties they satisfy and try to distinguish between these semantics by looking at the requirements they meet. A particular important property turned out to be Cumulative Monotony: If ''alpha squiggley horizontal right perpendicular beta'' then: ''alpha squiggley horizontal right perpendicular gamma'' iff ''alpha AND beta squiggley horizontal right perpendicular gamma''. We show that, while both two-valued semantics COMP and STABLE are not cumulative monotone, their three-valued extensions COMP3 and the well-founded semantics WFS are. They actually satisfy a further property, namely Rational Monotony: If ''not alpha squiggley horizontal right perpendicular inverted left perpendicular beta'' and ''alpha squiggley horizontal right perpendicular gamma'', then ''alpha AND beta squiggley horizontal right perpendicular gamma'' While Baral, Lobo and Minker's GWFS, an extension of WFS, handles floating conclusions, it is not cumulative. We define another extension of WFS which handles some sort of floating conclusions and still is cumulative but not rational: this may be seen as an attempt to solve a problem recently raised by Makinson, Brewka and Schlechta.